[CL] Question about partial functions and "The king of France is bald"
martinobal at gmail.com
Fri Jan 19 16:10:10 CST 2007
Thanks for the quick reply, John.
I see, CL can be applied to many different ontologies. So, where does
the concept of "bottom" I described come from? KIF and IKL do have
associated ontologies, right? Is there a name for the kind of ontology
where partial functions are totalised by using Bottom? I recall I
liked this concept of a neutral element, because it seems to reflect
natural language much better than, say, the Russellian version of
On 1/19/07, John F. Sowa <sowa at bestweb.net> wrote:
> That feature is not available in CL, but you could
> define something that would give you the equivalent:
> > If I got it right, there's an element called "Bottom",
> > so that partial functions can be defined, and if there's
> > no referent for a particular argument, the function
> > evaluates to bottom.
> All functions in CL are total. However, CL has no built-in
> ontology. Therefore, you can use the name Bottom for some
> undefined entity. And then you can assert whatever axioms
> you please about Bottom in order to make Bottom behave the
> way you like.
> Another possibility is to have a different bottom for every
> function -- in fact, you could use the name of the function as
> its own bottom. For example, given any partial function f(x),
> 1. Define a dyadic relation f(x,y) which agrees with f(x)=y
> for all values on which f(x) is defined and false when
> f(x) is undefined.
> 2. Then define a function with the same name f by the following
> For all x, f(x)=f if and only if f(x,f(x)) is false.
> As a result of this definition, the total function f(x) has the
> value f when the original partial function f(x) is undefined.
> This is an example of the CL philosophy. It gives you enough
> flexibility to define such features instead of requiring them
> to be built in.
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